Learning good image priors is of utmost importance for the study of vision, computer vision and image processing applications. Learning priors and optimizing over whole images can lead to tremendous computational challenges. In contrast, when we work with small image patches, it is possible to learn priors and perform patch restoration very efficiently. This raises three questions - do priors that give high likelihood to the data also lead to good performance in restoration? Can we use such patch based priors to restore a full image? Can we learn better patch priors? In this work we answer these questions. We compare the likelihood of several patch models and show that priors that give high likelihood to data perform better in patch restoration. Motivated by this result, we propose a generic framework which allows for whole image restoration using any patch based prior for which a MAP (or approximate MAP) estimate can be calculated. We show how to derive an appropriate cost function, how to optimize it and how to use it to restore whole images. Finally, we present a generic, surprisingly simple Gaussian Mixture prior, learned from a set of natural images. When used with the proposed framework, this Gaussian Mixture Model outperforms all other generic prior methods for image denoising, deblurring and inpainting.

/pdf/from-learning-models-of-natural-image-patches-to-whole-image-25iz5mt23l.pdf

From learning models of natural image patches to whole image restoration

In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented.

Image Denoising Using the Higher Order Singular Value Decomposition

Source separation using single channel ICA

https://www.commsp.ee.ic.ac.uk/~nikolao/pdf/Elsevier_fusion.pdf

Pixel-based and region-based image fusion schemes using ICA bases

This work addresses the problem of signal-dependent noise removal in images. An adaptive nonlinear filtering approach in the orthogonal transform domain is proposed and analyzed for several typical noise environments in the DCT domain. Being applied locally, that is, within a window of small support, DCT is expected to approximate the Karhunen-Loeve decorrelating transform, which enables effective suppression of noise components. The detail preservation ability of the filter allowing not to destroy any useful content in images is especially emphasized and considered. A local adaptive DCT filtering for the two cases, when signal-dependent noise can be and cannot be mapped into additive uncorrelated noise with homomorphic transform, is formulated. Although the main issue is signal-dependent and pure multiplicative noise, the proposed filtering approach is also found to be competing with the state-of-the-art methods on pure additive noise corrupted images.

/pdf/locally-adaptive-dct-filtering-for-signal-dependent-noise-2ozd9b5ebm.pdf

Locally Adaptive DCT Filtering for Signal-Dependent Noise Removal

Sparse coding is a method for finding a neural network representation of multidimensional data in which each of the components of the representation is rarely ignorantly active at the same time. The representation is closely related to independent component analysis (ICA). In this paper, we introduced the basic principle of ICA and have investigated the capabilities of sparse coding shrinkage in the field of image denoising. We have also performed practical implementation of sparse code shrinkage (SCS) and applied to the image denoising. We have seen that SCS outperforms basic denoising methods such as wiener filtering, median filtering and Independent Component Analysis (ICA) applied to image denoising.

Image Denoising by Sparse Code Shrinkage

Sparse coding is a method for finding a neural network representation of multidimensional data in which each of the components of the representation is rarely ignorantly active at the same time. The representation is closely related to Independent Component Analysis (ICA). In this paper, we introduced the basic principle of ICA and have investigated the capabilities of ICA in the field of image edge detection. We have also performed practical implementation of ICA and applied to edge detection through the basis as the sample template. We have seen that ICA outperforms basic edge detection methods such as Canny, Robert, Sobel and Prewitt. Keywords-sparse coding; Independent Component Analysis; edge detection; basis; sample model.

Gewen Kang

Papers

Image Denoising by Sparse Code Shrinkage

Edge Detection Using Sparse Coding Method